MRI is an imaging modality that is widely used to visualize soft tissue structures, such as brain tissue structures, muscle tissue structures, heart tissue structures, etc. Due to its capability of using contrast weightings based on physiological functions, traditional MRI has led to the development of fMRI, which requires the acquisition of time series information, i.e., a set of images of a region of interest acquired at different time points. An important consideration in fMRI is the total scan time required to obtain an accurate representation of the region of interest, which, in turn, determines the temporal resolution of the time series information. The temporal resolution must be adequate for accurately rendering time-varying properties of the region of interest, such as changes in local blood flow and/or oxygenation. For a conventional fMRI imaging system, the temporal resolution is typically in the range of about 2 to 2.5 seconds for whole-brain coverage. Thus, for fMRI, an increase in the temporal resolution would be desirable. Because fMRI techniques typically acquire a set of Fourier transform measurements for use in image reconstruction, one possible way of increasing the temporal resolution of fMRI is to reduce the amount of Fourier transform information obtained for each image in the time series.
One technique for reducing the amount of Fourier transform information obtained for image reconstruction is based on the known theory of Compressed Sensing (CS). Using CS, images can be accurately reconstructed from a set of incomplete, possibly random, Fourier transform measurements. The Fourier transform measurements are regarded as being incomplete in the sense that a discrete Fourier transform (DFT) of the Fourier transform measurements does not accurately recover the images. The known Nyquist-Shannon sampling theorem specifies that, in order to reconstruct an image with high accuracy, it is necessary to acquire the same number of Fourier transform measurements as the spatial resolution of the image. However, using CS, accurate image reconstruction can be achieved by obtaining fewer Fourier transform measurements than the number specified by the Nyquist-Shannon sampling theorem.